A little more information is needed to begin to help you out:
1. What do you mean when you say that it's hanging?
- does the screen still show the lock screen?
- are you using a PIN or pattern unlock or just a regular swipe?
- is the screen just going blank?
2. Same applies to the problem when receiving a call
- does the call get interrupted or does it continue normally?
- does it only happen if the lock screen was on? What about if the screen is already on/unlocked when the call comes in?
- do any of the buttons still work when experiencing the problem?

If it is a similar issue that I and others have had, it may be related to the stock browser. When the screen goes off after timing out. Then you try to wake the phone it will freeze off and not let you turn back on. I switched to the Chrome browser and haven't had the issue since.

As for the phone portion I'm not sure there. More info may help.

This all being said I'm not sure if the issues are the same or not... Hope it helps sorry you are having issues with your new phone

1.) Yes, hanging in the sense, the screen still show the lock screen, when am trying to unlock it.
2.) I locked the screen, someone called me, but i didnt get an incoming call but for called subscriber its ringing.
3.) Even Unlocking the screen using regular swipe is not working well; 3-4 times i need to do regular swipe then it unlocks.

For the first problem, what applications have you installed on the phone? Deleting things from the SD card won't remove any applications you've installed. In fact, if an app is expecting to find something there, it might make things worse.

For the second, I'm not sure what you mean by "getting switched off." Do you mean you turn the screen off, or actually power down the phone? If the phone is powered down, I don't think there's any way it can power back up by itself. Do you mean the phone reboots? That means it shuts down and restarts immediately, all by itself?

While it's possible you have a defective phone, it's more likely something you've installed is causing the problems.

My first thought is that you've installed some application that is causing the error. I suggest removing any apps you installed, rebooting the phone, and see if that solves it. If not, try a factory reset.

If removing the apps does solve the problem, add them back one or two at a time, use the phone for a couple of days, and see if the problem begins after you install a particular app.

If none of the above works, take the phone back to where you bought it.

I'm having this problem too, started very recently (and I'm currently roaming in the US from the UK, and it is worse while I am here). It either locks or it just reboots randomly. It seems to be a function of temporarily losing network connection on the S3 (which seems to happen all the time here). I would say it started since I upgraded to the latest firmware level. I don't add software that often.

I have Nexus 10 and that is also prone to randomly rebooting. It doesn't have 3G access but I think it is also if the wifi signal is low. So I wonder whether this is an issue with the latest version of Android.

This is just speculation and not sure whether it's useful, but I'm waiting for the next firmware rev to see if it fixes it.

Uninstalled few apps, didnt work.
Then Factory reset given and no apps installed further. It is like new Phone.
Also made Window & Transition animation scale to .5x
Checked Force GPU rendering and set Limit background processes to 'At most 4 processes'.

Why did you set the limit on background processes? Android keeps lots of thing in the background. By limiting background processes to four, you may be forcing Android to kill processes it needs to work correctly, or that an open application needs, making that application crash and take Android with it.

There's a reasons these are "developer" options. They're intended for testing application functionality, not for normal usage of the phone.(Yes, I understand there may be valid reasons to set some of them, but they can have undesirable side-effects, too.)

I'd start by resetting any and all developer options to their normal settings, reboot the phone, and see what happens. If you're still getting crashes on a completely stock configuration, then it's time to take the phone back to where you bought it and ask for an exchange.

Factory reset the phone.
Don't play with the developer settings.
Don't install any goofy task managers.
If it still reboots or locks up, shuts down or restarts, it is defective. Get a repaired or replaced.

Update of Jelly bean over internet or using kies have created this problem , there could be bugs in the software update file due to which hanging problem appears in the phone , so please visit service center where they will update phone software through using ODIN where is it will erase existing each software file and update bug free software .

if problem still continues then there could be hardware issue (chip / board malfunctioning) which will be resolved by samsung free of cost if your phone is under warranty ....

The first thing any service center will do is a factory reset. 9 times out of 10 (or maybe 99 times out of a 100) that will solve the problem. Why pay a service center $60 to do what you can do for free?

If a factory reset doesn't fix it, then you can take it to a service center. And yes, back up whatever you can before doing a factory reset.